Principles and psychophysics of Active Inference in anticipating a dynamic, switching probabilistic bias

Laurent Perrinet, ChloƩ Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain


http://invibe.net/LaurentPerrinet/Presentations/2018-04-05_BCP_talk

Principles and psychophysics of Active Inference in anticipating a dynamic, switching probabilistic bias

Laurent Perrinet, ChloƩ Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain

Outline

  1. Motivation

  2. Raw psychophysical results
  3. The Bayesian Changepoint Detector
  4. Results using the BCP

Motivation - a Real-life example

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Eye Movements

Motivation - Random-length block design

Motivation - Random-length block design

Outline

  1. Motivation
  2. Raw psychophysical results

  3. The Bayesian Changepoint Detector
  4. Results using the BCP

Raw psychophysical results - Random-length block design

Raw psychophysical results

Raw psychophysical results - Fitting eye movements

Raw psychophysical results - Fitting eye movements

Raw psychophysical results

Raw psychophysical results

Raw psychophysical results

Raw psychophysical results

Outline

  1. Motivation
  2. Raw psychophysical results
  3. The Bayesian Changepoint Detector

  4. Results using the BCP

The Bayesian Changepoint Detector

The Bayesian Changepoint Detector

The Bayesian Changepoint Detector

The Bayesian Changepoint Detector

The Bayesian Changepoint Detector

The Bayesian Changepoint Detector

Bayesian Changepoint Detector

  1. Initialize
    • $P(r_0)= S(r)$ or $P(r_0=0)=1$ and
    • $ν^{(0)}_1 = ν_{prior}$ and $χ^{(0)}_1 = χ_{prior}$
  2. Observe New Datum $x_t$
  3. Evaluate Predictive Probability $Ļ€_{1:t} = P(x |ν^{(r)}_t,χ^{(r)}_t)$
  4. Calculate Growth Probabilities $P(r_t=r_{t-1}+1, x_{1:t}) = P(r_{t-1}, x_{1:t-1}) Ļ€^{(r)}_t (1āˆ’H(r^{(r)}_{t-1}))$
  5. Calculate Changepoint Probabilities $P(r_t=0, x_{1:t})= \sum_{r_{t-1}} P(r_{t-1}, x_{1:t-1}) π^{(r)}_t H(r^{(r)}_{t-1})$
  6. Calculate Evidence $P(x_{1:t}) = \sum_{r_{t-1}} P (r_t, x_{1:t})$
  7. Determine Run Length Distribution $P (r_t | x_{1:t}) = P (r_t, x_{1:t})/P (x_{1:t}) $
  8. Update Sufficient Statistics :
    • $ν^{(0)}_{t+1} = ν_{prior}$, $χ^{(0)}_{t+1} = χ_{prior}$
    • $ν^{(r+1)}_{t+1} = ν^{(r)}_{t} +1$, $χ^{(r+1)}_{t+1} = χ^{(r)}_{t} + u(x_t)$
  9. Perform Prediction $P (x_{t+1} | x_{1:t}) = P (x_{t+1}|x_{1:t} , r_t) P (r_t|x_{1:t})$
  10. go to (2)

The Bayesian Changepoint Detector

The Bayesian Changepoint Detector

Outline

  1. Motivation
  2. Raw psychophysical results
  3. The Bayesian Changepoint Detector
  4. Results using the BCP

Results using the BCP - inference with BCP

Results using the BCP - inference with BCP

Results using the BCP - inference with BCP

Results using the BCP - fit with BCP

Results using the BCP - fit with BCP

Results using the BCP - fit with BCP

Results using the BCP - fit with BCP

Results using the BCP - fit with BCP

Principles and psychophysics of Active Inference in anticipating a dynamic, switching probabilistic bias

Laurent Perrinet, ChloƩ Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain